Scale symmetry in quantum wetteric/Talks/Cosmo/Y1517...¢  2015-08-24¢  crossover in quantum gravity

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  • Scale symmetry inScale symmetry in quantum gravityquantum gravity

  • quantum gravity with scalar field –

    the role of scale symmetry

  • fluctuations inducefluctuations induce running couplingsrunning couplings

    violation of scale symmetryviolation of scale symmetry well known in QCD or standard modelwell known in QCD or standard model

    http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCNzurrualsYCFYMW2wodrxcAbQ&url=http%3A%2F%2Fbackreaction.blogspot.com%2F2007%2F12%2Fasymptotic-freedom-and-coupling.html&ei=5CGBVdzsKYOt7Aavr4DoBg&bvm=bv.96041959,d.ZGU&psig=AFQjCNH_9d8w-ZfnXNbwLx0zHXBJRU9etg&ust=1434612575477703

  • functional renormalization :functional renormalization : flowing actionflowing action

    Wikipedia

  • Quantum Quantum scalescale symmetrysymmetry

    quantumquantum fluctuationsfluctuations violateviolate scalescale symmetrysymmetry runningrunning dimensionlessdimensionless couplingscouplings at at fixedfixed pointspoints , , scalescale symmetrysymmetry isis exactexact !!

  • CrossoverCrossover in in quantumquantum gravitygravity

  • OriginOrigin of of massmass

    UV UV fixedfixed point : point : scalescale symmetrysymmetry unbrokenunbroken all all particlesparticles areare masslessmassless

    IR IR fixedfixed point : point : scalescale symmetrysymmetry spontaneouslyspontaneously brokenbroken, , massive massive particlesparticles , , masslessmassless dilatondilaton

    crossovercrossover : : explicitexplicit massmass scalescale μμ important important

    approximate SM fixed point : approximate SM fixed point : approximate scale symmetryapproximate scale symmetry spontaneously brokenspontaneously broken, , massive particles , almost massive particles , almost masslessmassless cosmoncosmon, tiny , tiny cosmoncosmon potentialpotential

  • Spontaneous breaking of scale symmetry

    expectation value of scalar field breaks scale symmetry spontaneously massive particles are compatible with scale symmetry in presence of massive particles : sign of exact scale symmetry is exactly massless Goldstone boson – the dilaton

  • Approximate scale symmetry near fixed points

    UV : approximate scale invariance of primordial fluctuation spectrum from inflation

    IR : cosmoncosmon is pseudo Goldstone boson of is pseudo Goldstone boson of spontaneously broken scale symmetry,spontaneously broken scale symmetry, tiny mass,tiny mass, responsible for dynamical Dark Energy

  • AsymptoticAsymptotic safetysafety

    ifif UV UV fixedfixed point point existsexists ::

    quantumquantum gravitygravity isis nonnon--perturbativelyperturbatively renormalizablerenormalizable !!

    S. Weinberg , M. ReuterS. Weinberg , M. Reuter

  • a predictiona prediction……

  • IR IR fixedfixed point in point in quantumquantum gravitygravity

    First positive First positive indicationindication fromfrom functionalfunctional renormalizationrenormalization flowflow withwith truncationtruncation ::

    fixedfixed point point effectiveeffective actionaction ::

    large fieldlarge field behavior of Fbehavior of F

  • PossiblePossible consequencesconsequences of of crossovercrossover in in quantumquantum gravitygravity

    Realistic model for inflation and dark energyRealistic model for inflation and dark energy with single scalar fieldwith single scalar field

  • Variable Variable GravityGravity

    quantumquantum effectiveeffective actionaction,, variationvariation yieldsyields fieldfield equationsequations

    MM22 RREinstein gravity :Einstein gravity :

  • Variable GravityVariable Gravity

    Scalar field coupled to gravityScalar field coupled to gravity Effective Planck mass depends on scalar fieldEffective Planck mass depends on scalar field Simple quadratic scalar potential involves intrinsic mass Simple quadratic scalar potential involves intrinsic mass μμ Nucleon and electron mass proportional to dynamical Nucleon and electron mass proportional to dynamical Planck massPlanck mass

  • running coupling Brunning coupling B

    B varies if intrinsic scale B varies if intrinsic scale µµ changeschanges similar to QCD or standard modelsimilar to QCD or standard model

    http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCNzurrualsYCFYMW2wodrxcAbQ&url=http%3A%2F%2Fbackreaction.blogspot.com%2F2007%2F12%2Fasymptotic-freedom-and-coupling.html&ei=5CGBVdzsKYOt7Aavr4DoBg&bvm=bv.96041959,d.ZGU&psig=AFQjCNH_9d8w-ZfnXNbwLx0zHXBJRU9etg&ust=1434612575477703

  • KinetialKinetial B : B : CrossoverCrossover betweenbetween twotwo fixedfixed pointspoints

    http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCNzurrualsYCFYMW2wodrxcAbQ&url=http%3A%2F%2Fbackreaction.blogspot.com%2F2007%2F12%2Fasymptotic-freedom-and-coupling.html&ei=5CGBVdzsKYOt7Aavr4DoBg&bvm=bv.96041959,d.ZGU&psig=AFQjCNH_9d8w-ZfnXNbwLx0zHXBJRU9etg&ust=1434612575477703

  • KinetialKinetial B : B : CrossoverCrossover betweenbetween twotwo fixedfixed pointspoints

    runningrunning couplingcoupling obeysobeys flowflow equationequation

    m : m : scalescale of of crossovercrossover cancan bebe exponentiallyexponentially larger larger thanthan intrinsicintrinsic scalescale μμ

  • InfraredInfrared fixedfixed pointpoint

    μ→μ→ 00 BB→→ 00

    no intrinsic mass scaleno intrinsic mass scale scale symmetryscale symmetry

  • UltravioletUltraviolet fixedfixed pointpoint

    μ→μ→ ∞∞

    kinetialkinetial divergesdiverges

    scalescale symmetrysymmetry withwith anomalousanomalous dimensiondimension σσ

  • RenormalizedRenormalized fieldfield at UV at UV fixedfixed pointpoint

    1 < 1 < σσ

    no no massmass scalescale

    deviationdeviation fromfrom fixedfixed pointpoint vanishesvanishes forfor μ→μ→ ∞∞

  • CosmologicalCosmological solutionsolution :: crossovercrossover fromfrom UV to IR UV to IR fixedfixed pointpoint

    DimensionlessDimensionless functionsfunctions as B as B dependdepend onlyonly on on ratioratio μμ//χχ .. IR: IR: μ→μ→0 , 0 , χ→∞χ→∞ UV: UV: μ→∞μ→∞ , , χ→χ→00

    Cosmology makes Cosmology makes

    crossover betweencrossover between

    fixed points byfixed points by

    variation of variation of χχ ..

  • Cosmological solutionCosmological solution

    derive field equation from effective action of derive field equation from effective action of variable gravityvariable gravity solve them for homogenous and isotropic solve them for homogenous and isotropic metric and scalar field metric and scalar field scalar field scalar field χχ vanishes in the infinite pastvanishes in the infinite past scalar field scalar field χχ diverges in the infinite futurediverges in the infinite future

  • No tiny dimensionless parametersNo tiny dimensionless parameters ( except gauge hierarchy )( except gauge hierarchy )

    one mass scaleone mass scale

    one time scale one time scale μμ--11 = 10 = 10 1010 yryr

    Planck mass does not appear as parameterPlanck mass does not appear as parameter Planck mass grows large dynamically

    μμ = 2 = 2 10 10 --33 33 eVeV

    Planck mass grows large dynamically

  • Particle massesParticle masses change with time change with time

    At SM fixed point : At SM fixed point : All particle masses ( except for neutrinos ) are All particle masses ( except for neutrinos ) are proportional to scalar field proportional to scalar field χχ .. Scalar field varies with time Scalar field varies with time –– so do particle masses.so do particle masses. Ratios of particle masses are independent of Ratios of particle masses are independent of χχ and and therefore remain constant.therefore remain constant. Compatibility with observational bounds on time Compatibility with observational bounds on time dependence of particle mass ratios.dependence of particle mass ratios. Dimensionless couplings are independent of Dimensionless couplings are independent of χχ ..

  • Four-parameter model

    model has four dimensionless parameters three in kinetial B : σ ~ 2.5 κ ~ 0.5 ct ~ 14 ( or m/μ )

    one parameter for present growth rate of neutrino mass over electron mass : γ ~ 8 + standard model particles and dark matter : sufficient for realistic cosmology from inflation to dark energy no more free parameters than ΛCDM

  • Cosmological solutionCosmological solution

    scalar field scalar field χχ vanishes in the infinite pastvanishes in the infinite past

    scalar field scalar field χχ diverges in the infinite futurediverges in the infinite future

  • Strange Strange evolutionevolution of of UniverseUniverse

    SonntagszeitungSonntagszeitung ZZüürich , rich , LaukenmannLaukenmann

  • Slow UniverseSlow Universe

    Asymptotic solution in Asymptotic solution in freeze frame :freeze frame :

    Expansion or shrinking always slow ,Expansion or shrinking always slow , characteristic time sca